Metrics to prove or disprove the need for additional DBA's?

We currently have 2 DBA’s, me and one other guy and we both feel the need for an additional resource (or two). I have had the conversation with my direct manager on this topic a couple different times, but am having difficulty in getting the notion sold. Most recently our manager shared with us that it is really good to come up with our “soft values” list of things that we want or feel we need to be doing, but what will really help is to come up with “hard values”, showing dollar savings. Could you help me in understanding first of all if our perceived need is legitimate, and if so, how do we go about coming up with this “hard values” list. I feel like we could come up with those things that we need to do in order to save the company money, but that could just get put at the front of our priorities list, and that much more stress on us in the process. To give you a high level look at our environment, here are the things that I am looking at in terms of what we are providing support for. >Production servers – 30+ Production Databases – 200+ SQL Versions – 2008/2008R2/2012, looking into 2014 now, and 2016 later in the year Applications(3rd party and home grown) – 20+ Application Teams Supported – 6 Virtualization – 75% virtualized 25% physical Clusters – 3+ more planned Replication – 1 distribution server, 2 subscription servers, 24 subscriptions, 6 publication servers, 12 publications Log shipping – 8 primaries +more planned, 4 secondaries + more planned, 49 log shipped databases + more planned Availability Groups – None at the moment, but exploring the possibility Average application upgrade/installs per year that drive version change or DBA resources – 2-3 Patching (SP, CU’s) – Non-existent at the moment unless an issue comes up Cumulative database size – 14TB+ Reporting Servers – One scale-out deployment consisting of 2 servers, neither of us are well versed in SSRS Analysis Server – Two servers, neither of us are well versed in SSAS What metrics should we use to prove or disprove the need for additional DBA's? My initial intention was demonstrating our current capacity vs. our planned projects and repeating tasks, but we need to demonstrate the ROI on hiring additional resources.